Abstract: Systems and/or methods that facilitate secure electronic communication of data are presented. A cryptographic component facilitates data encryption, data decryption, and/or generation of digital signatures, associated with messages. The cryptographic component includes a randomized exponentiation component that facilitates decryption of data and/or generation of digital signatures by exponentiating exponents associated with messages. A random number is generated and utilized to randomize the value of a message. After an exponentiation is performed on the randomized message value, intermediate results can be analyzed to determine if there was error in the exponentiation. If there was no error in the exponentiation, a final value of the exponentiation is determined and provided as output as decrypted data or a digital signature; if there is error, an “error” output can be provided.

Abstract: Systems and/or methods that facilitate secure electronic communication of data are presented. A cryptographic component facilitates securing data associated with messages in accordance with a cryptographic protocol. The cryptographic component includes a randomized exponentiation component that facilitates decryption of data and generation of digital signatures by exponentiating exponents associated with messages. An exponent is divided into more than one subexponent at an exponent bit that corresponds to a random number. Exponentiation of the first subexponent can be performed based on a left-to-right-type of exponentiation algorithm, and exponentiation of the second subexponent can be performed based on a right-to-left square-and-multiply-type of exponentiation algorithm. The final value is based on the exponentiations of the subexponents and can be decrypted data or a digital signature, which can be provided as an output.

Abstract: Data processing method and related devices for determining the result of a first type of operation involving an operand in an electronic entity comprising a non-volatile storage unit, includes the following steps: converting a data, derived from at least one key portion designed to be used with the operand in the first type of operation, into a key data adapted to be used with the operand in a second type of operation; storing the key data in the non-volatile storage unit; reading in the non-volatile storage unit the key data; performing the second type of operation with the read key data and the operand.